Finite Group Databasebeta

← C2×#13080576 #15630282

Subgroups — C2×#13080576 #15630282

Order 2816.

2514 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623257C211yesmaximal, characteristic, complemented
2C2×#10623207C211yesmaximal, characteristic, complemented
3#13080576C2116yesmaximal, direct product factor
4C2×#10622390C211yesmaximal, characteristic, complemented
5C2×#10622418C211yesmaximal, characteristic, complemented
6C2×#10622697C211yesmaximal, characteristic, complemented
7C2×#10622395C211yesmaximal, characteristic, complemented
8C2×#10622420C211yesmaximal, characteristic, complemented
9C2×#10622670C211yesmaximal, characteristic, complemented
10C2×#10622424C211yesmaximal, characteristic, complemented
11C2×#10622386C211yesmaximal, characteristic, complemented
12C2×#10622324C211yesmaximal, characteristic, complemented
13C2×#10622319C211yesmaximal, characteristic, complemented
14C2×#10622416C211yesmaximal, characteristic, complemented
15C2×D11×#102C211yesmaximal, characteristic, complemented
16C2×C11×#489C211yesmaximal, characteristic, complemented
17C22×#4343—21no—
18C22×#4343C2211yescharacteristic
19C22×D4×D11C2211yescharacteristic
20C2×C11×C4⋊Q8C2211yescharacteristic, complemented
21C2×C11×#124C2211yescharacteristic
22C2×#66999—21no—
23C2×#66999C2211yescharacteristic
24C22×#4325C2211yescharacteristic, complemented
25C2×#66991C2211yescharacteristic
26C22×#4323C2211yescharacteristic
27C22×D88C2211yescharacteristic
28C22×#4313C2211yescharacteristic, complemented
29C22×C8×D11C2211yescharacteristic
30#10623257—24no—
31#10623257C2218yescomplemented
32#10623207—24no—
33#10623207C2218yescomplemented
34C2×#66948C2211yescharacteristic
35C2×#66948C2211yescharacteristic, complemented
36C2×#66947—21no—
37C2×#66947—21no—
38C2×C4⋊C4×D11C2211yescharacteristic
39C2×C4⋊C4×D11C2211yescharacteristic, complemented
40C2×#66937—21no—
41C2×#66936—21no—
42C2×#66935—21no—
43C2×C22⋊C4×D11—21no—
44C2×C4×D44C2211yescharacteristic
45C2×C4×D44C2211yescharacteristic
46C2×C4×D44C2211yescharacteristic, complemented
47C11×#489C2218yescomplemented
48C2×C11×#103C2211yescharacteristic, complemented
49C2×C11×#103C2211yescharacteristic, complemented
50C2×C11×#102C2211yescharacteristic
51C2×C11×#102C2211yescharacteristic
52C2×C11×#97C2211yescharacteristic, complemented
53C2×#66899C2211yescharacteristic, complemented
54C2×#66896C2211yescharacteristic
55C2×#66885C2211yescharacteristic
56C2×#66885C2211yescharacteristic, complemented
57C2×(C2×D11)⋊C8C2211yescharacteristic
58C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
59C2×#66881C2211yescharacteristic, complemented
60#10622697C2218yescomplemented
61#10622670C2218yescomplemented
62C2×#66873C2211yescharacteristic
63C2×#66873C2211yescharacteristic
64C2×#66872C2211yescharacteristic, complemented
65C2×#66872C2211yescharacteristic, complemented
66C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
67#10622424C2218yescomplemented
68#10622420C2218yescomplemented
69#10622418C2218yescomplemented
70#10622416C2218yescomplemented
71#10622395C2218yescomplemented
72#10622390C2218yescomplemented
73#10622386C2218yescomplemented
74D11×#102C2218yescomplemented
75#10622324C2218yescomplemented
76#10622319C2218yescomplemented
77C24×D11—21no—
78C22×Q8×C11—21no—
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C22×C22⋊D11—21no—
82C22×C22⋊D11—21no—
83C2×#4343—28no—
84C2×#4343—22no—
85C2×#4343—24no—
86C2×#4343—42no—
87C2×#4343—48no—
88C2×#4343C2314yes—
89C2×D4×D11—24no—
90C2×D4×D11—22no—
91C2×D4×D11—42no—
92C2×D4×D11C2314yes—
93C22×D44—21no—
94C22×D44—21no—
95C22×D44—21no—
96C22×D44D411yescharacteristic
97C22×D44C2311yescharacteristic
98C22×D44C2311yescharacteristic
99C22×C4×D11—21no—
100C22×C4×D11—21no—
101C22×C4×D11—21no—
102C22×C4×D11—21no—
103C22×C4×D11—21no—
104C22×C4×D11C2311yescharacteristic
105C22×C4×D11C2311yescharacteristic
106C22×C8×C11C2311yescharacteristic
107C22×C8×C11C2311yescharacteristic
108C11×C4⋊Q8—22no—
109C11×C4⋊Q8C2314yescomplemented
110C11×#124—22no—
111C11×#124C2314yes—
112C2×C11×C4⋊C4—21no—
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C22⋊C4—21no—
116C2×C11×C22⋊C4—21no—
117C2×C42×C11C2311yescharacteristic
118C2×C22⋊Dic11—21no—
119#66999—22no—
120#66999—28no—
121#66999C2314yes—
122C2×#4325—42no—
123C2×#4325C2314yescomplemented
124#66991—22no—
125#66991C2314yes—
126C2×#4323—42no—
127C2×#4323C2314yes—
128C2×(C2×D11)⋊C4—21no—
129C2×(C2×D11)⋊C4—21no—
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4D411yescharacteristic
134C2×(C2×D11)⋊C4D411yescharacteristic
135C2×C4⋊Dic11D411yescharacteristic
136C2×C4⋊Dic11C2311yescharacteristic
137C2×C4⋊Dic11C2311yescharacteristic
138C2×Dic11⋊C4—21no—
139C2×Dic11⋊C4—21no—
140C2×Dic11⋊C4—21no—
141C22×C11⋊C8C2311yescharacteristic
142C22×C11⋊C8C2311yescharacteristic
143C2×D88—24no—
144C2×D88C2314yes—
145C2×#4313—42no—
146C2×#4313C2314yescomplemented
147C2×C8×D11—42no—
148C2×C8×D11C2314yes—
149#66948—22no—
150#66948—22no—
151#66948C2314yes—
152#66948C2314yescomplemented
153#66947—28no—
154#66947—28no—
155C4⋊C4×D11—22no—
156C4⋊C4×D11—22no—
157C4⋊C4×D11C2314yes—
158C4⋊C4×D11C2314yescomplemented
159#66937—28no—
160#66936—28no—
161#66935—28no—
162C22⋊C4×D11—28no—
163C4×D44—22no—
164C4×D44—22no—
165C4×D44D414yes—
166C4×D44C2314yes—
167C4×D44C2314yes—
168C4×D44C2314yescomplemented
169C11×#103C2314yescomplemented
170C11×#103C2314yescomplemented
171C11×#102C2314yes—
172C11×#102C2314yes—
173C11×#97C2314yescomplemented
174#66899C2314yescomplemented
175#66896C2314yes—
176#66885C2314yes—
177#66885C2314yescomplemented
178(C2×D11)⋊C8C2314yes—
179(C2×D11)⋊C8C2314yescomplemented
180#66881C2314yescomplemented
181#66873C2314yes—
182#66873C2314yes—
183#66872C2314yescomplemented
184#66872C2314yescomplemented
185C4⋊(C11⋊C8)C2314yescomplemented
186C2×#3306—111nomaximal, Sylow
187C24×C11—21no—
188C23×D11—21no—
189C23×D11—21no—
190C23×D11—24no—
191C23×D11—44no—
192C23×D11—44no—
193C23×D11—82no—
194C23×D11C2×D411yescharacteristic
195C23×D11C2×D411yescharacteristic
196C2×Q8×C11—21no—
197C2×Q8×C11—24no—
198C2×Q8×C11—22no—
199C2×Q8×C11—22no—
200C2×Q8×C11—44no—
201C2×Q8×C11C2412yes—
202C2×D4×C11—21no—
203C2×D4×C11—22no—
204C2×D4×C11—22no—
205C2×D4×C11C2412yes—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2411yescharacteristic
212C2×C22⋊D11—24no—
213C2×C22⋊D11—24no—
214C2×C22⋊D11—44no—
215C2×C22⋊D11—82no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11C2×D411yescharacteristic
219C22×Dic11C2×D411yescharacteristic
220#4343—28no—
221#4343—44no—
222#4343—48no—
223#4343—432no—
224D4×D11—28no—
225D4×D11—44no—
226D4×D11—48no—
227C2×D44—24no—
228C2×D44—24no—
229C2×D44—24no—
230C2×D44—24no—
231C2×D44—21no—
232C2×D44—21no—
233C2×D44—22no—
234C2×D44—22no—
235C2×D44—22no—
236C2×D44—44no—
237C2×D44—44no—
238C2×D44—44no—
239C2×D44C2×D414yes—
240C2×D44#4114yescomplemented
241C2×D44C2412yes—
242C2×D44C2412yes—
243C2×C4×D11—24no—
244C2×C4×D11—24no—
245C2×C4×D11—24no—
246C2×C4×D11—24no—
247C2×C4×D11—24no—
248C2×C4×D11—22no—
249C2×C4×D11—22no—
250C2×C4×D11—22no—
251C2×C4×D11—22no—
252C2×C4×D11—44no—
253C2×C4×D11—44no—
254C2×C4×D11—44no—
255C2×C4×D11—44no—
256C2×C4×D11—82no—
257C2×C4×D11C2×D412yes—
258C2×C4×D11C2×D412yes—
259C2×C4×D11C2412yes—
260C2×C4×D11C2412yes—
261C2×C8×C11—22no—
262C2×C8×C11—22no—
263C2×C8×C11C2412yes—
264C2×C8×C11C2412yes—
265C11×C4⋊C4—21no—
266C11×C4⋊C4—21no—
267C11×C4⋊C4—24no—
268C11×C4⋊C4C2412yes—
269C11×C4⋊C4C2412yes—
270C11×C22⋊C4—24no—
271C11×C22⋊C4—24no—
272C42×C11C2×D412yes—
273C42×C11C2412yes—
274C22⋊Dic11—24no—
275#4325—44no—
276#4323—44no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4—24no—
280(C2×D11)⋊C4—24no—
281(C2×D11)⋊C4—24no—
282(C2×D11)⋊C4C2×D414yes—
283(C2×D11)⋊C4C2×D414yes—
284C4⋊Dic11—21no—
285C4⋊Dic11—21no—
286C4⋊Dic11C2×D414yes—
287C4⋊Dic11C2412yes—
288C4⋊Dic11C2412yes—
289Dic11⋊C4—24no—
290Dic11⋊C4—24no—
291Dic11⋊C4—24no—
292C2×C11⋊C8—22no—
293C2×C11⋊C8—22no—
294C2×C11⋊C8C2412yes—
295C2×C11⋊C8C2412yes—
296D88—28no—
297#4313—44no—
298C8×D11—44no—
299C2×#547—111no—
300C2×#546—111no—
301#3306—1116no—
302C2×#489D1111yescharacteristic, complemented
303C2×#481—111no—
304C2×#483—111no—
305C2×#476—111no—
306C2×#469—111no—
307C2×#465—111no—
308C2×#463—111no—
309C2×#449—111no—
310C2×#447—111no—
311C2×#442—111no—
312C2×#435—111no—
313C2×#417—111no—
314C22×#102—111no—
315C23×C11—22no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11—42no—
319C23×C11C22×D411yescharacteristic
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—24no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—48no—
329C22×D11—42no—
330C22×D11—42no—
331C22×D11—42no—
332C22×D11—42no—
333C22×D11—42no—
334C22×D11—48no—
335C22×D11—84no—
336C22×D11—816no—
337C22×D11AGL(1,ℤ/8)14yes—
338C22×D11C22×D412yes—
339C22×D11C22×D412yes—
340Q8×C11—22no—
341Q8×C11—22no—
342Q8×C11—48no—
343Q8×C11—42no—
344D4×C11—22no—
345D4×C11—22no—
346D4×C11—42no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—42no—
353C2×C4×C11—42no—
354C2×C4×C11—42no—
355C2×C4×C11C22×D412yes—
356C2×C4×C11C22×D412yes—
357C2×C4×C11C22×D411yescharacteristic
358C2×C4×C11C2×#4112yes—
359C2×C4×C11H(5,𝔽2)12yes—
360C2×C4×C11C2511yescharacteristic
361C22⋊D11—48no—
362C22⋊D11—84no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—42no—
368C2×Dic11—42no—
369C2×Dic11C22×D412yes—
370C2×Dic11C22×D412yes—
371D44—28no—
372D44—24no—
373D44—22no—
374D44—22no—
375D44—22no—
376D44—48no—
377D44—48no—
378D44—48no—
379D44—42no—
380D44C2×#4114yescomplemented
381C4×D11—24no—
382C4×D11—24no—
383C4×D11—22no—
384C4×D11—22no—
385C4×D11—22no—
386C4×D11—22no—
387C4×D11—48no—
388C4×D11—48no—
389C4×D11—48no—
390C4×D11—48no—
391C4×D11—84no—
392C8×C11—22no—
393C8×C11—22no—
394C11⋊C8—22no—
395C11⋊C8—22no—
396C22×#41—111no—
397C22×#41—221no—
398C23×D4—111no—
399C22×SD16—111no—
400C22×D8—111no—
401C22×D8—111no—
402C22×M16—111no—
403C23×C8—111no—
404#547—118no—
405#547—224no—
406#546—118no—
407#546—224no—
408C2×C4⋊Q8C2×D1111yescharacteristic, complemented
409C2×#124C2×D1111yescharacteristic
410C2×#123—221no—
411C2×#123—221no—
412C2×#123—221no—
413C2×C22⋊Q8—111no—
414C2×C22⋊Q8—221no—
415C2×#121—111no—
416C2×#121—111no—
417C2×#121—111no—
418C2×#121—221no—
419C2×#120—221no—
420C2×C4×D4—111no—
421C2×C4×D4—111no—
422C2×C4×D4—111no—
423C22×C4⋊C4—111no—
424C22×C4⋊C4—111no—
425C22×C22⋊C4—221no—
426#489C2×D1118yescomplemented
427#483—118no—
428#481—118no—
429#476—118no—
430#469—118no—
431#465—118no—
432#463—118no—
433#449—118no—
434#447—118no—
435#442—118no—
436#435—118no—
437C2×#106—111no—
438C2×#106—111no—
439C2×#106—111no—
440C2×C4⋊C8—111no—
441#417—118no—
442C2×#103—111no—
443C2×#103C2×D1111yescharacteristic, complemented
444C2×#103C2×D1111yescharacteristic, complemented
445C2×#102—111no—
446C2×#102—111no—
447C2×#102—111no—
448C2×#102—111no—
449C2×#102—111no—
450C2×#102—118no—
451C2×#102C2×D1111yescharacteristic
452C2×#102C2×D1111yescharacteristic
453C2×C22⋊C8—111no—
454C2×C22⋊C8—111no—
455C2×#97C2×D1111yescharacteristic, complemented
456C22×C11—42no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—84no—
460C22×C11#54612yes—
461C22×C11C2×AGL(1,ℤ/8)12yes—
462C22×C11#57712yes—
463C22×C11C23×D411yescharacteristic
464C2×D11—22no—
465C2×D11—28no—
466C2×D11—22no—
467C2×D11—24no—
468C2×D11—22no—
469C2×D11—22no—
470C2×D11—22no—
471C2×D11—44no—
472C2×D11—48no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—816no—
479C2×D11—84no—
480C2×D11C2×AGL(1,ℤ/8)14yes—
481C4×C11—22no—
482C4×C11—22no—
483C4×C11—42no—
484C4×C11—42no—
485C4×C11—42no—
486C4×C11#54612yes—
487C4×C11C22×#4111yescharacteristic
488C4×C11C2×H(5,𝔽2)11yescharacteristic
489Dic11—22no—
490Dic11—22no—
491Dic11—42no—
492Dic11—42no—
493C25—221no—
494C2×#41—114no—
495C2×#41—222no—
496C2×#41—228no—
497C2×#41—224no—
498C2×#41—442no—
499C2×#41—448no—
500C22×Q8—21no—
501C22×Q8C22×D1111yescharacteristic
502C22×D4—114no—
503C22×D4—111no—
504C22×D4—111no—
505C22×D4—111no—
506C22×D4—221no—
507C22×D4—221no—
508C22×D4—221no—
509C22×D4—222no—
510C22×D4—221no—
511C22×D4—224no—
512C22×D4—221no—
513C22×D4—442no—
514C22×D4C22×D1111yescharacteristic
515C23×C4—111no—
516C23×C4—111no—
517C23×C4—221no—
518C23×C4—221no—
519C23×C4—221no—
520C23×C4—221no—
521C23×C4—221no—
522C2×SD16—114no—
523C2×SD16—442no—
524C2×D8—114no—
525C2×D8—114no—
526C2×D8—224no—
527C2×D8—442no—
528C2×M16—114no—
529C2×M16—442no—
530C22×C8—111no—
531C22×C8—111no—
532C22×C8—114no—
533C22×C8—442no—
534C22×C8C22×D1111yescharacteristic
535C22×C8C22×D1111yescharacteristic
536C4⋊Q8—22no—
537C4⋊Q8C22×D1114yescomplemented
538#124—22no—
539#124C22×D1114yes—
540#123—228no—
541#123—228no—
542#123—228no—
543C22⋊Q8—114no—
544C22⋊Q8—228no—
545C22⋊Q8—222no—
546#121—114no—
547#121—114no—
548#121—114no—
549#121—228no—
550#121—222no—
551#121—222no—
552#121—222no—
553#120—228no—
554C4×D4—114no—
555C4×D4—114no—
556C4×D4—114no—
557C4×D4—114no—
558C4×D4—222no—
559C4×D4—222no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—111no—
562C2×C4⋊C4—111no—
563C2×C4⋊C4—111no—
564C2×C4⋊C4—114no—
565C2×C4⋊C4—114no—
566C2×C4⋊C4—222no—
567C2×C4⋊C4—222no—
568C2×C4⋊C4—221no—
569C2×C4⋊C4—221no—
570C2×C4⋊C4—221no—
571C2×C4⋊C4C22×D1111yescharacteristic
572C2×C4⋊C4C22×D1111yescharacteristic
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—111no—
576C2×C22⋊C4—111no—
577C2×C22⋊C4—228no—
578C2×C22⋊C4—221no—
579C2×C22⋊C4—221no—
580C2×C22⋊C4—221no—
581C2×C22⋊C4—221no—
582C2×C22⋊C4—221no—
583C2×C22⋊C4—221no—
584C2×C42C22×D1111yescharacteristic
585#106—114no—
586#106—114no—
587#106—114no—
588C4⋊C8—114no—
589#103—114no—
590#103C22×D1114yescomplemented
591#103C22×D1114yescomplemented
592#102—114no—
593#102—114no—
594#102—114no—
595#102—114no—
596#102—114no—
597#102C22×D1114yes—
598#102C22×D1114yes—
599C22⋊C8—114no—
600C22⋊C8—114no—
601#97C22×D1114yescomplemented
602C2×C11—82no—
603C2×C11#330614yescomplemented
604C2×C11C2×#54611yescharacteristic
605C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
606C2×C11C2×#57711yescharacteristic
607D11—24no—
608D11—42no—
609D11—44no—
610D11—82no—
611C24—21no—
612C24—111no—
613C24—111no—
614C24—224no—
615C24—221no—
616C24—221no—
617C24—444no—
618C24—444no—
619C24—882no—
620#41—228no—
621#41—444no—
622#41—448no—
623#41—4432no—
624C2×Q8—21no—
625C2×Q8—24no—
626C2×Q8—22no—
627C2×Q8—22no—
628C2×Q8—44no—
629C2×Q8C23×D1112yes—
630C2×D4—21no—
631C2×D4—22no—
632C2×D4—22no—
633C2×D4—114no—
634C2×D4—114no—
635C2×D4—112no—
636C2×D4—112no—
637C2×D4—224no—
638C2×D4—224no—
639C2×D4—224no—
640C2×D4—224no—
641C2×D4—224no—
642C2×D4—228no—
643C2×D4—224no—
644C2×D4—221no—
645C2×D4—221no—
646C2×D4—222no—
647C2×D4—222no—
648C2×D4—222no—
649C2×D4—444no—
650C2×D4—444no—
651C2×D4—444no—
652C2×D4—444no—
653C2×D4—448no—
654C2×D4—444no—
655C2×D4—882no—
656C2×D4C23×D1112yes—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—111no—
661C22×C4—111no—
662C22×C4—112no—
663C22×C4—112no—
664C22×C4—112no—
665C22×C4—112no—
666C22×C4—224no—
667C22×C4—224no—
668C22×C4—224no—
669C22×C4—222no—
670C22×C4—222no—
671C22×C4—222no—
672C22×C4—222no—
673C22×C4—221no—
674C22×C4—221no—
675C22×C4—224no—
676C22×C4—224no—
677C22×C4—444no—
678C22×C4—444no—
679C22×C4—444no—
680C22×C4—444no—
681C22×C4—882no—
682C22×C4D4×D1111yescharacteristic
683C22×C4D4×D1111yescharacteristic
684C22×C4C23×D1111yescharacteristic
685SD16—444no—
686D8—228no—
687D8—444no—
688M16—444no—
689C2×C8—22no—
690C2×C8—22no—
691C2×C8—112no—
692C2×C8—112no—
693C2×C8—222no—
694C2×C8—222no—
695C2×C8—444no—
696C2×C8C23×D1112yes—
697C2×C8C23×D1112yes—
698C4⋊C4—24no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—114no—
702C4⋊C4—112no—
703C4⋊C4—112no—
704C4⋊C4—224no—
705C4⋊C4—224no—
706C4⋊C4—224no—
707C4⋊C4—221no—
708C4⋊C4—221no—
709C4⋊C4C23×D1112yes—
710C4⋊C4C23×D1112yes—
711C22⋊C4—24no—
712C22⋊C4—24no—
713C22⋊C4—114no—
714C22⋊C4—114no—
715C22⋊C4—224no—
716C22⋊C4—224no—
717C22⋊C4—224no—
718C22⋊C4—224no—
719C22⋊C4—224no—
720C22⋊C4—224no—
721C42D4×D1112yes—
722C42C23×D1112yes—
723C11C2×#330611yescharacteristic, complemented, Sylow
724C23—22no—
725C23—42no—
726C23—42no—
727C23—42no—
728C23—114no—
729C23—112no—
730C23—112no—
731C23—222no—
732C23—222no—
733C23—222no—
734C23—222no—
735C23—222no—
736C23—222no—
737C23—224no—
738C23—222no—
739C23—448no—
740C23—448no—
741C23—442no—
742C23—442no—
743C23—442no—
744C23—442no—
745C23—442no—
746C23—884no—
747C23—8816no—
748C23C2×D4×D1111yescharacteristic
749Q8—22no—
750Q8—22no—
751Q8—48no—
752Q8—42no—
753D4—22no—
754D4—22no—
755D4—42no—
756D4—114no—
757D4—228no—
758D4—222no—
759D4—222no—
760D4—222no—
761D4—224no—
762D4—448no—
763D4—448no—
764D4—448no—
765D4—448no—
766D4—442no—
767D4—884no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—112no—
777C2×C4—112no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—222no—
783C2×C4—222no—
784C2×C4—224no—
785C2×C4—224no—
786C2×C4—222no—
787C2×C4—222no—
788C2×C4—448no—
789C2×C4—448no—
790C2×C4—448no—
791C2×C4—448no—
792C2×C4—442no—
793C2×C4—442no—
794C2×C4—884no—
795C2×C4C2×D4×D1112yes—
796C2×C4C2×D4×D1112yes—
797C2×C4C2×D4×D1111yescharacteristic
798C2×C4#41×D1112yes—
799C2×C4#6704212yes—
800C2×C4C24×D1111yescharacteristic
801C8—22no—
802C8—22no—
803C8—222no—
804C8—222no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—84no—
809C22—114no—
810C22—228no—
811C22—222no—
812C22—222no—
813C22—222no—
814C22—224no—
815C22—222no—
816C22—222no—
817C22—444no—
818C22—448no—
819C22—442no—
820C22—442no—
821C22—442no—
822C22—442no—
823C22—442no—
824C22—8816no—
825C22—884no—
826C22#1062320712yes—
827C22D11×AGL(1,ℤ/8)12yes—
828C22#1062330912yes—
829C22C22×D4×D1111yescharacteristic
830C4—22no—
831C4—22no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—222no—
836C4—222no—
837C4—442no—
838C4—442no—
839C4#1062320712yes—
840C4C2×#41×D1111yescharacteristic
841C4C2×#6704211yescharacteristic
842C2—82no—
843C2—224no—
844C2—442no—
845C2—444no—
846C2—882no—
847C2#1308057614yesdirect product factor
848C2C2×#1062320711yescharacteristic
849C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
850C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#489C2
socleC23×C11C22×D4
hypercenterC2×#489D11
hypocenterC11C2×#3306
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#10623257C2semidirect
2. C2×#10623207C2semidirect
3. #13080576C2direct (N × H)
4. C2×#10622390C2semidirect
5. C2×#10622418C2semidirect
6. C2×#10622697C2semidirect
7. C2×#10622395C2semidirect
8. C2×#10622420C2semidirect
9. C2×#10622670C2semidirect
10. C2×#10622424C2semidirect
11. C2×#10622386C2semidirect
12. C2×#10622324C2semidirect
13. C2×#10622319C2semidirect
14. C2×#10622416C2semidirect
15. C2×D11×#102C2semidirect
16. C2×C11×#489C2semidirect
20. C2×C11×C4⋊Q8C22semidirect
24. C22×#4325C22semidirect
28. C22×#4313C22semidirect
31. #10623257C22semidirect
33. #10623207C22semidirect
35. C2×#66948C22semidirect
39. C2×C4⋊C4×D11C22semidirect
46. C2×C4×D44C22semidirect
47. C11×#489C22semidirect
48. C2×C11×#103C22semidirect
49. C2×C11×#103C22semidirect
52. C2×C11×#97C22semidirect
53. C2×#66899C22semidirect
56. C2×#66885C22semidirect
58. C2×(C2×D11)⋊C8C22semidirect
59. C2×#66881C22semidirect
60. #10622697C22semidirect
61. #10622670C22semidirect
64. C2×#66872C22semidirect
65. C2×#66872C22semidirect
66. C2×C4⋊(C11⋊C8)C22semidirect
67. #10622424C22semidirect
68. #10622420C22semidirect
69. #10622418C22semidirect
70. #10622416C22semidirect
71. #10622395C22semidirect
72. #10622390C22semidirect
73. #10622386C22semidirect
74. D11×#102C22semidirect
75. #10622324C22semidirect
76. #10622319C22semidirect
109. C11×C4⋊Q8C23semidirect
123. C2×#4325C23semidirect
146. C2×#4313C23semidirect
152. #66948C23semidirect
158. C4⋊C4×D11C23semidirect
168. C4×D44C23semidirect
169. C11×#103C23semidirect
170. C11×#103C23semidirect
173. C11×#97C23semidirect
174. #66899C23semidirect
177. #66885C23semidirect
179. (C2×D11)⋊C8C23semidirect
180. #66881C23semidirect
183. #66872C23semidirect
184. #66872C23semidirect
185. C4⋊(C11⋊C8)C23semidirect
240. C2×D44#41semidirect
302. C2×#489D11semidirect
380. D44C2×#41semidirect
408. C2×C4⋊Q8C2×D11semidirect
426. #489C2×D11semidirect
443. C2×#103C2×D11semidirect
444. C2×#103C2×D11semidirect
455. C2×#97C2×D11semidirect
537. C4⋊Q8C22×D11semidirect
590. #103C22×D11semidirect
591. #103C22×D11semidirect
601. #97C22×D11semidirect
603. C2×C11#3306semidirect
723. C11C2×#3306semidirect
847. C2#13080576direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106232572
C2×#106232072
#130805762
C2×#106223902
C2×#106224182
C2×#106226972
C2×#106223952
C2×#106224202
C2×#106226702
C2×#106224242
C2×#106223862
C2×#106223242
C2×#106223192
C2×#106224162
C2×D11×#1022
C2×C11×#4892
C2×#330611